Elastodynamics-encoded recurrent neural networks for characterization of anisotropic elastic constants and stiffness...

Physics-informed neural networks (PINNs) have been applied to elastodynamic inverse problems. However, the soft enforcement of the physics through the loss function leads to convergence difficulties and limited interpretability, particularly for anisotropic materials with coupled elastic constants. This work proposes a physics-encoded recurrent neural network (ERNN) that hard-codes the elastodynamic partial differential equations directly into the network architecture. We derive an explicit mapping between the anisotropic elastic wave propagation and standard RNN operations, establishing that the time recurrent model is mathematically equivalent to an RNN with physics-defined weights corresponding to the six independent elastic constants. Different from PINNs that approximate solutions through black-box function fitting, the ERNN embeds the exact governing equations into its structure, ensuring physical consistency at every time step. Training minimizes the mismatch between predicted and observed ultrasonic wavefields, enabling spatially resolved inversion of elastic constants for material characterization and stiffness degradation imaging. Numerical validations demonstrate that the ERNN accurately inverts elastic constants of both orthotropic and generally anisotropic materials with relative errors below 2%. Further experiments on single, double, and complex stiffness degradation scenarios show that the ERNN can localize, image, and quantitatively assess various degradation patterns. Moreover, the framework is extended to Kirchhoff-Love plate theory, demonstrating its generality and practical applicability to thin-plate structural health monitoring. The physics-interpretable ERNN framework opens new possibilities for ultrasonic nondestructive evaluation and structural health monitoring.